Explanation for Question 20 From the Math (No Calc) Section on the 2017 October Sat
Question 20 says the graph of the linear function F is shown in the 2 X, Y plane above the graph of the linear function, 3 G which is not shown is perpendicular to the graph of F and passes 4 through the 0.13. What is the value of G of zero? 5 So to find the value of G of zero we're first going to have 6 to find the equation for G of X, 7 and the way we're going to do that is by using the Y equals 8 MX plus B formula where N represents the slope of the line and B 9 represents the y-intercept. The first thing we can find of G of X is 10 the slope. And we can do that by finding the slope of FX 11 and then finding the opposite reciprocal of that. 12 And that's because perpendicular lines have opposite reciprocal slopes. 13 So if you notice the slope of F of X is just negative two, 14 because the rise is negative two, it goes down to, 15 and the run is positive one. 16 So since the slope of F of X is negative to the opposite, 17 reciprocal of that is positive one half. 18 That way we know that M in this case is equal to positive one 19 half, but we still need to find B. 20 And the way we're going to do that is by plugging in one, 21 three, a point that we know passes through G of X, 22 and we're going to solve for B. So let's just plug that in. 23 We know three is equal to one half times one plus B. 24 So we know that B is equal to two and a half. 25 Now we have both the M value one half, 26 and the B value two and a half, 27 which can also be written as five over two. 28 And with that, we can plug in zero for X to find what G 29 of zero is equal to. So Y is equal to one half time, 30 zero, which is just zero plus two and a half, 31 which means that Y is equal to two and a half. 32 And G of zero is two and a half or 500.
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